First Week of the Fall Term 2011 – Mathematics Graduate School

Gradient Flows by Luigi Ambrosio

It’s the second week of school, but with a bank holiday last Monday (09/12/11), graduate school started up slowly. It will take until next week until everyone is finally registered to all of their classes. It took me a while to do so as well, because they changed up the system from a program that you installed on your computer to an online version. The online version is better, but you need to know where to go. I finally registered to my classes last Tuesday. I have three this semester:

Topics in Geometric Analysis: This class is with my thesis advisor and we will be exploring gradient flows in metric spaces. We will be using Luigi Ambrosio’s book of the same title. It promises to be an interesting class. Although, it’s not exactly what I’d like to do in my thesis, it’s getting there. I’d like more measure theory, but luckily, my advisor is doing research in the field. There are six students in the class, but only 4 were registered on Monday. I don’t know if the other two will be registering, my guess is yes. Two of my classmates are the other graduate students of my advisor. We are all going to a workshop in Hsinchu in Differential Geometry  on Saturday. Since I work most Saturdays, it’s not really a problem getting up. It will be a break from the norm, and I have a keen interest in Differential Geometry.

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Doing A Graduate Degree In Taiwan

NTNU Main building on Heping Dong Rd.

I just read Fili’s most recent post about his stint at a Taiwanese university (I couldn’t tell which from the post). Having been an international student at NTNU, in the graduate program of Mathematics since ’09, I have different things to report. Granted, I am studying in sciences at the graduate level, so the classes are ultimately very small. I have 4 students in one class and 2 in another.

Still, there are some important points to remember when you think about doing a graduate program in Taiwan.

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Mathematical Teaching Methods

Snake Lemma, via Wikipedia
Snake Lemma, via Wikipedia


It seems to me quite logical on how math classes should proceed. The professor presents some theory, with theorems and their demonstration, as well as definitions and propositions, before venturing into a slew of examples. For some reason, this is completely absent from my classes in Taiwan. The examples. I don’t know what these profs are thinking, but examples are paramount for students to understand some of the theory. OK, my complex analysis prof is good. he gives examples and answers questions well¹.

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Rainy Mathematical Days

Lamy Safari fountain pens
Lamy Safari fountain pens²


The rain has finally abated. I love the rain in Canada, but I hate it here. Why? You just get wet all the time. You get wet when you get on the scooter, when you drive around, and when you get off. Rain gear does wonders, but it’s annoying to have to carry it around and wait for it to dry. Also, driving in the rain is a lot more dangerous. I tend to be really careful.

Temperatures have cooled down significantly. It’s no longer 30C, but only 24C³. It’s getting a bit chilly when riding on the scooter. I’ll need to take a scarf.

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Second Week of School

This is a non-commutative ring
This is a non-commutative ring

It’s the second week of school and my classmates have become quite curious about me⁵. I usually hang out with Mary and John. John showed me the two science bookstores near Taida⁴. He’s also an older student, though he lives in LongTan, Taoyuan, and commutes everyday by bus.

The kids in my Modern Algebra class wanted to know if I needed the book. I informed them that I had already ordered a copy and that there were quite a few softcover Algebra [Hungerford, Springer-Verlag] available at the Newton book store. Naturally, they already knew this.

One classmate copied all of his PDF math books onto the shared computer. That’s going to be really fun, because he also has the solutions of the exercises in Measure and Integral. The Complex Variables [Berenstein & Gay, Springer Verlag]¹ and Measure books will be copied this week. I’ll copy the PDF books tomorrow³.

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Non-Riemannian Integration

Paul Halmos Measure Theory from Springer
Paul Halmos' Measure Theory from Springer

We started seeing the Riemann-Stieltjes integral today as well as a reminder on rectifiable curves¹. We didn’t see much⁴, but it made me interested in other forms of measure. Appropriately, I bought Halmos’ Measure Theory [vol 18, Springer-Verlag] for $6.18 last week. It’s going to be useful. It was a good idea to spend some money on reference books.

I’m still kind of surprised at the amount of books that I got for $120². Today, my classmates organized a photocopying session. By this, I mean that they will organize to have Measure and Integral by Wheeden photocopied and bound for everyone who wants it. I hopped on the photocopying bandwagon, as this book costs about $70 new³. I can always order it if I like it. It seems that the real analysis professor is basing his course on that book.

I read up on the Daniell integral, Lebesgue integral. I came across this in Henri Lebesgue’s biography on Wikipedia.

Lebesgue integration has the beautiful property that every bounded function defined over a bounded interval with a Riemann integral also has a Lebesgue integral, and for those functions the two integrals agree. But there are many functions with a Lebesgue integral that have no Riemann integral.


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Graduate Trash and First Impressions

Apparently, a few months ago, there was trash all over the graduate student area at NTNU. It was so bad that the professors and staff talked about how to clean up your own trash for about 20 minutes today. It was kind of funny. Charlotte told me that most graduate students are babied and really don’t know what is going on. She told me that a student had left her with actual mice because of teh amount of trash that she had left there without cleaning up.

I also learned that I have a sort of office. It’s a communal office that I share with other students. This means that I can easily stash my bike there. That’s a relief. Charlotte told me that they have a lot of free space on the 4th floor. That made me want to request other office space, but I won’t. I don’t mind being around other students, it’s going to be fun.

The staff and older PhD students are all very nice, as well as the new students who aren’t too shy. Shida specializes in the education of mathematics and the history of math. Those aren’t my areas of interest, but I’ve been told that I’ll have an easier time studying there than at NTU.

The big thing are the qualifying exams that everyone has to sit in order to get into PhD programs in US universities. Charlotte is taking hers in about a month. I will take them next year in May. There is a chance that if I do well in those exams, I could get a “passage au doctorat”, which means that I’d get a M.Sc and PhD instead of just a PhD by just doing about 3 years. That’s pretty exciting, but that means that this year, it will get intense.

There are quite a few interesting classes. Above all, it’s Real Analysis and Complex Analysis that I will focus on, as Functional Analysis isn’t taught this year. I’ll have to take a Modern Algebra class as well in order to prepare fully for the exams. All the professors that I’ve talked with assured me that this should be my goal. This will make admission into a US university easier as well.

In more mundane tasks, I’ve secured a locker for myself as well. They have given me the access card and I still have one paper to fill in for them.

My wife ended up doing a lot of extra work for professors. This is totally of on top of what she has to do with her classes. It drains a lot of her time. I was curious to find out if this was the same in math. Charlotte assures me that this isn’t the case. She has been studying for her PhD for two years and she never does anything extra. Well she does, but it’s usually small things.

I’m really happy that I’ll be studying there with Charlotte nearby. She’s French and I love the fact that I can speak French with her all the time. I’ve only met a few French-speakers in Taiwan and I’ve never really been in contact with them for long amounts of time.

BTW, Charlotte is studying Mathematical Education and she is translating Sanskrit math problems into English.

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